Not Korean but Japanese, I like the Sana moisturiser and the Curel intensive moisture facial cream
I personally love hyaluronic acid, always use it under moisturisers (I’ve used a few and tbh I think they’re all kind of the same, the ordinary or inkey list ones are nice and inexpensive) and it makes a big difference for me! You just have to make sure your skin is slightly damp when you put it on and you don’t let it dry out before you put your moisturiser on